$L^p$-estimates for the Schr\"odinger equation associated to the harmonic oscillator

TL;DR

This paper derives new Strichartz estimates for the Schrödinger equation linked to the harmonic oscillator and Laplacian, using embeddings between Lebesgue and Triebel-Lizorkin spaces.

Contribution

It introduces novel Strichartz estimates for these equations by employing embeddings between Lebesgue and Triebel-Lizorkin spaces.

Findings

Established new Strichartz estimates for harmonic oscillator Schrödinger equation

Extended estimates to Laplacian Schrödinger equation

Utilized embeddings between Lebesgue and Triebel-Lizorkin spaces

Abstract

In this paper we obtain some Strichartz estimates for the Schr\"odinger equation associated to the harmonic oscillator and the Laplacian. Our main tool will be some embeddings between Lebesgue spaces and suitable Triebel-Lizorkin spaces.